2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54258In this first paper we begin the application of variational methods to renormalisable asymptotically free field theories, using the Gross-Neveu model as a laboratory. This variational method has been shown to lead to a numerically convergent sequence of approximations for the anharmonic oscillator. Here we perform a sample calculation in lowest orders, which shows the superficially disastrous situation of variational calculations in quantum field theory, and how in the large-$N$ limit all difficulties go away, as a warm up exercise for the finite-$N$ case and for QCD.20 pages, includes 4-uuencoded figures, uses revtex one minor corection in the tex source to include properly figHigh Energy Physics - Theorytext